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LGCU (Learning Gamma CUSUM) is an R package for designing and analyzing CUSUM control charts applied to Gamma distributions with guaranteed performance. The package provides methods for:
The methodologies implemented follow the work of Madrid-Alvarez, García-Díaz, and Tercero-Gómez (2024), ensuring rigorous statistical foundations and practical applications in industrial quality control.
To install the package from GitHub:
# Install devtools if not already installed
install.packages("devtools")
# Install LGCU from GitHub
::install_github("your_github_username/LGCU") devtools
To load the package:
library(LGCU)
GICARL_CUSUM_down(alpha, beta, alpha_est, beta_est, beta_ratio, H_minus, H_delta, m)
# Example:
GICARL_CUSUM_down(alpha = 1, beta = 1, alpha_est = 1, beta_est = 1,
beta_ratio = 1/2.5, H_minus = -2.792, H_delta = 0, m = 100)
GICARL_CUSUM_up(alpha, beta, alpha_est, beta_est, beta_ratio, H_plus, H_delta, m)
# Example:
GICARL_CUSUM_up(alpha = 1, beta = 1, alpha_est = 1.2, beta_est = 0.8,
beta_ratio = 2, H_plus = 6.5081, H_delta = 2.9693, m = 100)
ARL_Clminus(alpha, beta, alpha0_est, beta0_est, known_alpha, beta_ratio, H_delta, H_minus, n_I, replicates, K_l, delay, tau)
# Example:
ARL_Clminus(
alpha = 1,
beta = 1,
alpha0_est = 1.067, # alpha = known_alpha
beta0_est = 0.2760, # Estimated Beta
known_alpha = TRUE,
beta_ratio = 1/2,
H_delta = 0.6946,
H_minus = -4.8272,
n_I = 500,
replicates = 1000,
K_l = 0.5,
delay = 25,
tau = 1
)
ARL_Clplus(alpha, beta, alpha0_est, beta0_est, known_alpha, beta_ratio, H_delta, H_plus, n_I, replicates, K_l, delay, tau)
# Example:
ARL_Clplus(
alpha = 1,
beta = 1,
alpha0_est = 1, # alpha = known_alpha
beta0_est = 1.1, # Estimated Beta
known_alpha = TRUE,
beta_ratio = 2,
H_delta = 4.2433,
H_plus = 8.7434,
n_I = 200,
replicates = 100,
K_l = 2,
delay = 25,
tau = 1
)
plot_GICCdown_chart(alpha, beta, beta_ratio, H_delta, H_minus, n_I, n_II, faseI, faseII, known_alpha)
# Example:
plot_GICCdown_chart(alpha = 3, beta = 1, beta_ratio = 1/2, H_delta = 0.9596, H_minus = -4.6901,
n_I = 100, n_II = 200, faseI = NULL, faseII = NULL, known_alpha = FALSE)
plot_GICCup_chart(alpha, beta, beta_ratio, H_delta, H_plus, n_I, n_II, faseI, faseII, known_alpha)
# Example:
plot_GICCup_chart(alpha = 1, beta = 1, beta_ratio = 2, H_delta = 0, H_plus = 5.16,
n_I = 100, n_II = 200, faseI = NULL, faseII = NULL, known_alpha = TRUE)
plot_GICC_chart2(alpha, beta, beta_ratio_plus, beta_ratio_minus, H_delta_plus, H_plus, H_delta_minus, H_minus, n_I, n_II, faseI, faseII, known_alpha)
# Example:
plot_GICC_chart2(alpha = 1, beta = 1, beta_ratio_plus = 2, beta_ratio_minus = 0.5,
H_delta_plus = 2.0, H_plus = 5.0, H_delta_minus = 1.5, H_minus = -4.5,
n_I = 100, n_II = 200, faseI = NULL, faseII = NULL, known_alpha = TRUE)
plot_GICCLdown_Chart(alpha, beta, beta_ratio, H_delta, H_minus, known_alpha, k_l, delay, tau, n_I, n_II, faseI, faseII)
# Example:
plot_GICCLdown_Chart(alpha = 1, beta = 1, beta_ratio = 1/2, H_delta = 4.2433, H_minus= -4.8257,
known_alpha = FALSE, k_l = 0.739588, delay = 25, tau = 1,
n_I = 200, n_II = 700, faseI = NULL, faseII = NULL)
plot_GICCLup_Chart(alpha, beta, beta_ratio, H_delta, H_plus, known_alpha, k_l, delay, tau, n_I, n_II, faseI, faseII)
# Example:
plot_GICCLup_Chart(alpha = 1, beta = 1, beta_ratio = 2, H_delta = 2.9819, H_plus = 6.5081,
known_alpha = TRUE, k_l = 2, delay = 25, tau = 1,
n_I = 200, n_II = 710, faseI = NULL, faseII = NULL)
plot_GICCL_chart2(alpha, beta, beta_ratio_plus, beta_ratio_minus, H_delta_plus, H_plus, H_delta_minus, H_minus, known_alpha, k_l, delay, tau, n_I, n_II, faseI, faseII)
# Example:
plot_GICCL_chart2(alpha = 1, beta = 1, beta_ratio_plus = 2, beta_ratio_minus = 0.5,
H_delta_plus = 3.0, H_plus = 6.5, H_delta_minus = 2.0, H_minus = -5.0,
known_alpha = TRUE, k_l = 2, delay = 25, tau = 1,
n_I = 200, n_II = 700, faseI = NULL, faseII = NULL)
H_delta
for Guaranteed
PerformancegetDeltaH_down(n_I, alpha, beta, beta_ratio, H_minus, a, b, ARL_esp, m, N_init, N_final, known_alpha)
# Example:
getDeltaH_down(n_I = 100, alpha = 1, beta = 1, beta_ratio = 1/2, H_minus = -4.1497,
a = 0.1, b = 0.05, ARL_esp = 370, m = 100, N_init = 10, N_final = 1000, known_alpha = TRUE)
getDeltaH_up(n_I, alpha, beta, beta_ratio, H_plus, a, b, ARL_esp, m, N_init, N_final, known_alpha)
# Example:
getDeltaH_up(n_I = 100, alpha = 1, beta = 1, beta_ratio = 2, H_plus = 6.8313,
a = 0.1, b = 0.05, ARL_esp = 370, m = 100, N_init = 10, N_final = 1000, known_alpha = TRUE)
H_delta
with LearninggetDeltaHL_down(n_I, alpha, beta, beta_ratio, H_minus, a, b, ARL_esp, replicates, N_init, N_final, known_alpha, K_l, delay, tau)
# Example:
getDeltaHL_down(n_I = 200, alpha = 1, beta = 1, beta_ratio = 1/1.5,
H_minus = -6.2913, a = 0.1, b = 0.05, ARL_esp = 370,
replicates = 10, N_init = 100, N_final = 1000, known_alpha = TRUE,
K_l = 0.7, delay = 25, tau = 1)
getDeltaHL_up(n_I, alpha, beta, beta_ratio, H_plus, a, b, ARL_esp, replicates, N_init, N_final, known_alpha, K_l, delay, tau)
# Example:
getDeltaHL_up(n_I = 200, alpha = 1, beta = 1, beta_ratio = 2,
H_plus = 6.8313, a = 0.1, b = 0.05, ARL_esp = 370,
replicates = 100, N_init = 100, N_final = 500, known_alpha = TRUE,
K_l = 2, delay = 25, tau = 1)
📖 Madrid-Alvarez, H. M., García-Díaz, J. C., & Tercero-Gómez, V. G. (2024). A CUSUM control chart for gamma distribution with guaranteed performance. Quality and Reliability Engineering International.
📖 Madrid-Alvarez, H. M., García-Díaz, J. C., & Tercero-Gómez, V. G. (2024). A CUSUM control chart for the Gamma distribution with cautious parameter learning. Quality Engineering.
If you would like to contribute, please follow these steps: 1. Fork
the repository. 2. Create a new branch
(feature-newFunction
). 3. Commit your changes. 4. Push to
the branch and submit a Pull Request.
This package is licensed under the MIT License, which means you are free to use, modify, and distribute the software, provided that the original copyright and license notice is included in all copies. This allows both open-source and commercial use.
For any questions or suggestions, please contact: 📩 <strong>harold.madrid@unisimon.edu.co</strong>
These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
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